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On-shell renormalization in the presence of mixing and instability

by
BerndKniehl (UHH)

We consider a system of unstable spin-1/2 fermions in a general
parity-nonconserving theory with intergeneration mixing and explain how to
renormalize its propagator matrix to all orders in perturbation theory. We
work in the pole scheme, in which the squares of the renormalized masses
are identified with the complex pole positions and the wave-function
renormalization (WFR) matrices are adjusted according to the
Lehmann-Symanzik-Zimmermann reduction formalism. Closed analytic
expressions for the pole-mass counterterms and WFR matrices in terms of
the self-energy functions are derived. In the Dirac case, we identify
residual degrees of freedom in the WFR matrices and propose an additional
renormalization condition to exploit them. By contrast, the WFR matrices
are uniquely fixed in the Majorana case. We demonstrate that, in the
presence of instability, the WFR matrices of the in and out states
bifurcate in the sense that they are no longer related by pseudo-Hermitian
conjugation.